# User:Dfeuer/Definition:Cone Compatible with Closed Ringoid

Let $(R,*,\circ)$ be a closed ringoid.
Let $C$ be a cone compatible with $*$.
Then $C$ is compatible with $(R,*,\circ)$ iff for each $x,y\in R$, the following holds:
$x,y \in C \implies x \circ y \in C$